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arXiv · 2602.10444

Chamfer-Linkage for Hierarchical Agglomerative Clustering

Kishen N Gowda·Willem Fletcher·MohammadHossein Bateni·Laxman Dhulipala·D Ellis Hershkowitz·Rajesh Jayaram·Jakub Łącki
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Abstract

Hierarchical Agglomerative Clustering (HAC) is a widely-used clustering method based on repeatedly merging the closest pair of clusters, where inter-cluster distances are determined by a linkage function. Unlike many clustering methods, HAC does not optimize a single explicit global objective; clustering quality is therefore primarily evaluated empirically, and the choice of linkage function plays a crucial role in practice. However, popular classical linkages, such as single-linkage, average-linkage and Ward's method show high variability across real-world datasets and do not consistently produce high-quality clusterings in practice. In this paper, we propose \emph{Chamfer-linkage}, a novel linkage function that measures the distance between clusters using the Chamfer distance, a popular notion of distance between point-clouds in machine learning and computer vision. We argue that Chamfer-linkage satisfies desirable concept representation properties that other popular measures struggle to satisfy. Theoretically, we show that Chamfer-linkage HAC can be implemented in $O(n^2)$ time, matching the efficiency of classical linkage functions. Experimentally, we find that Chamfer-linkage consistently yields higher-quality clusterings than classical linkages such as average-linkage and Ward's method across a diverse collection of datasets. Our results establish Chamfer-linkage as a practical drop-in replacement for classical linkage functions, broadening the toolkit for hierarchical clustering in both theory and practice.

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Kishen N Gowda, Willem Fletcher, MohammadHossein Bateni, Laxman Dhulipala, D Ellis Hershkowitz, Rajesh Jayaram, Jakub Łącki. 2026-02-11. Chamfer-Linkage for Hierarchical Agglomerative Clustering. https://arxiv.org/abs/2602.10444

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